#' targetQg.ltmle
#'
#' Function that targets estimates of Q to solve the EIF. Fits a single logistic
#' fluctuation regression of c(Q2n, L2) on relevant offsets and so-called
#' clever covariates.
#'
#' @param A0 A \code{vector} treatment delivered at baseline.
#' @param A1 A \code{vector} treatment deliver after \code{L1} is measured.
#' @param L2 A \code{vector} outcome of interest.
#' @param Q2n A \code{vector} of estimates of Q_{2,0}
#' @param Q1n A \code{vector} of estimates of Q_{1,0}
#' @param g1n A \code{vector} of estimates of g_{1,0}
#' @param g0n A \code{vector} of estimates of g_{0,0}
#' @param abar A \code{vector} of length 2 indicating the treatment assignment
#' that is of interest.
#' @param tolQ A \code{numeric}
#' @param return.models A \code{boolean} indicating whether the fluctuation model should be
#' returned with the output.
#' @importFrom SuperLearner trimLogit
#'
#' @return A list with named entries corresponding to the estimators of the
#' fluctuated nuisance parameters evaluated at the observed data values. If
#' \code{return.models = TRUE} output also includes the fitted fluctuation model.
targetQg.ltmle <- function(
A0, A1, L2, Q2n, Q1n, g1n, g0n, abar, tolQ, return.models, ...
){
#-------------------------------------------
# making outcomes for logistic fluctuation
#-------------------------------------------
# scale L2, Q2n, Q1n to be in (0,1)
L2.min <- min(L2); L2.max <- max(L2)
Q2n.min <- min(Q2n); Q2n.max <- max(Q2n)
Q1n.min <- min(Q1n); Q1n.max <- max(Q1n)
# scale L2
L2s <- (L2 - L2.min)/(L2.max - L2.min)
# scale Q2n for when it's an offset with L2 as outcome
Q2ns<- (Q2n - L2.min)/(L2.max - L2.min)
Q1ns <- (Q1n - L2.min)/(L2.max - L2.min)
flucOut <- c(Q2ns, L2s)
#-------------------------------------------
# making offsets for logistic fluctuation
#-------------------------------------------
flucOff <- c(
SuperLearner::trimLogit(Q1ns, trim = tolQ),
SuperLearner::trimLogit(Q2ns, trim = tolQ)
)
#-------------------------------------------
# making covariates for fluctuation
#-------------------------------------------
flucCov <- c(
# (L2.max - L2.min)*as.numeric(A0 == abar[1]) * (1/g0n), # for Q2n as outcome, logit(Q1n) offset
as.numeric(A0 == abar[1]) * (1/g0n), # for Q2n as outcome, logit(Q1n) offset
# (L2.max - L2.min)*as.numeric(A0==abar[1] & A1==abar[2]) / (g0n * g1n) # for L2 as outcome, logit(Q2n) as covariate
as.numeric(A0==abar[1] & A1==abar[2]) / (g0n * g1n) # for L2 as outcome, logit(Q2n) as covariate
)
#-------------------------------------------
# making covariates for prediction
#-------------------------------------------
# getting the values of the clever covariates evaluated at
# \bar{A} = abar
predCov <- c(
# (L2.max - L2.min)*1/g0n, # all A0 == abar[1]
1/g0n, # all A0 == abar[1]
# (L2.max - L2.min)*1/(g0n * g1n) # all c(A0,A1) = abar
1/(g0n * g1n) # all c(A0,A1) = abar
)
#-------------------------------------------
# fitting fluctuation submodel
#-------------------------------------------
flucmod <- suppressWarnings(glm(
formula = "out ~ offset(fo)",
data = data.frame(out = flucOut, fo = flucOff, fc = flucCov),
weights = fc,
family = binomial()
))
#--------------------------------------------
# get predictions back using predCov
#--------------------------------------------
# vector of nuisance parameters
# just set out = 0 in newdata so predict.glm does not complain
etastar <- predict(
flucmod, newdata = data.frame(out = 0, fo = flucOff, fc = predCov),
type = "response"
)
#------------------------------------------------------------
# assign etastar values to corresponding nuisance parameters
#------------------------------------------------------------
# length of output
n <- length(A0)
# first n entries are Q1nstar and transform back to original scale
Q1nstar <- etastar[(1):(n)]*(L2.max - L2.min) + L2.min
# next n entries are Q2nstar and transform back to original scale
Q2nstar <- etastar[(n+1):(2*n)]*(L2.max - L2.min) + L2.min
#----------------
# return
#----------------
out <- list(
Q1nstar = Q1nstar, Q2nstar = Q2nstar,
flucmod = NULL
)
if(return.models){
out$flucmod = flucmod
}
return(out)
}
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